Skein Categories in Non-semisimple Settings
Abstract
We introduce a version of skein categories which depends on a tensor ideal in a ribbon category, thereby extending the existing theory to the setting of non-semisimple TQFTs. We obtain modified notions of skein algebras of surfaces and skein modules of 3-cobordisms for non-semisimple ribbon categories. We prove that these skein categories built from ideals coincide with factorization homology, shedding new light on the similarities and differences between the semisimple and non-semisimple settings. As a consequence, we get a skein-theoretic description of factorization homology for a large class of balanced braided categories in Pr, precisely all those which are expected to induce an oriented categorified 3-TQFT.
- Publication:
-
arXiv e-prints
- Pub Date:
- June 2024
- DOI:
- 10.48550/arXiv.2406.08956
- arXiv:
- arXiv:2406.08956
- Bibcode:
- 2024arXiv240608956B
- Keywords:
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- Mathematics - Quantum Algebra;
- Mathematics - Category Theory;
- Mathematics - Geometric Topology;
- 18M15;
- 57K31
- E-Print:
- 29 pages. Comments welcome!